Number systems Groups of Numbers • In doing arithmetic and algebra, we work with several groups o f numbers.

NATURAL or COUNTING NUMBERS: The numbers 1, 2, 3, 4, . . . are called natural or counting numbers . WHOLE NUMBERS : The numbers 0, 1, 2, 3, . . . are called whole numbers. INTEGERS: The numbers . . . — 2, -1, 0, 1, 2, . . . are called integers . NEGATIVE INTEGERS : The numbers . . . — 3, —2, -1 are called negative integers . POSITIVE INTEGERS : The natural numbers are sometimes called th e positive integers . RATIONAL NUMBERS: Fractions, such as 3/2 or 7/8, are called rational numbers. Since a number such as 5 may be written as all integers are rational numbers . IRRATIONAL NUMBERS : Another type of number is an irrational number. Examples of irrational numbers are lj" and 7r . REAL NUMBERS: Real numbers consist of all rational and irrationa l numbers. Typically most standardized exams use only real numbers , which are the numbers you are used to using .

PRIME NUMBERS : A prime number is a number that can be evenly divided by only itself and 1 . For example, 19 is a prime numbe rbecause it can be evenly divided only by 19 and 1, but 21 is not aprime number because 21 can be evenly divided by other numbers ( 3and 7) . The only even prime number is 2 ; thereafter, any even numbe rmay be divided evenly by 2 . Zero and 1 are not prime numbers. Th efirst ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 . ODD NUMBERS : Odd numbers are whole numbers not divisible ,by 2 : 1,3,5,7, . . . EVEN NUMBERS : Even numbers are numbers divisible by 2: 0, 2, 4 , 6, . . . COMPOSITE NUMBERS: A composite number is a number divisible b y more than just 1 and itself: 4, 6, 8, 9, 10, 12, 14, 15, . . . SQUARES: Squares are the result when numbers are multiplied b y themselves : (2 . 2 = 4), (3 • 3 = 9) ; 1, 4, 9, 16, 25, 36 . . . CUBES: Cubes are the result when numbers are multiplied b y themselves twice: (2 . 2 . 2 = 8), (3 • 3 . 3 = 27) ; 1, 8, 27 . Signed Numbers (Positive Numbers and Negative Numbers ) Number Lines • On a number line, numbers to the right of 0 are positive . Numbers to the left of 0 are negative, as follows .

etc. I etc. -3

I

I-

I

I

2 -1 0 +1 +2 +3 Given any two numbers on a number line, the one on the right is always larger, regardless of its sign (positive or negative) . Note that fractions may also be placed on a number line .